A superior representation method for piecewise linear functions

Han-Lin Li*, Hao Chun Lu, Chia Hui Huang, Nian Ze Hu

*Corresponding author for this work

Research output: Contribution to journalArticle

22 Scopus citations


Many nonlinear programs can be piecewisely linearized by adding extra binary variables. For the last four decades, several techniques of formulating a piecewise linear function have been developed. By expressing a piecewise linear function with m+1 break points, the current method requires us to use m additional binary variables and 4m constraints, which causes heavy computation when m is large. This study proposes a superior way of expressing the same piecewise linear function, where only [log 2m] binary variables and 8 + 8[log 2m] additive constraints are used. Various numerical experiments demonstrate that the proposed method is more computationally efficient than current methods.

Original languageEnglish
Pages (from-to)314-321
Number of pages8
JournalINFORMS Journal on Computing
Issue number2
StatePublished - 1 Mar 2009


  • Integer
  • Mathematics
  • Piecewise linear
  • Programming

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